Question

A plane is flying 2000 feet above sea level toward a mountain as shown. The pilot observes the top of the mountain to be a = 16° above the horizontal, then immediately flies the plane at an angle of ß = 20° above horizontal. The airspeed of the plane is 100 mph. After 5 minutes, the plane is directly above the top of the mountain. How high is the plane above the top of the mountain (when it passes over)? What is the height of the mountain? Round to the nearest 10 feet. a ] h 2000 ft Height of plane above mountain feet Mountain height = feet

Answer 1

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B A Ja B D F E a = 16 B = 20 AF =DE= 2000 ft C is the top of mountain CE is the height of mountain

100 mp h. Thi apud of flight = เว onc hon = 100 mi Distance travels travels 5 minutu = 8.33 mi. in = 100 x 5 60 50x5 Distanu ic, AB= 8.33. → convichu RAABD BD Sin B= Opposite sich typotius AB Sin 20 = BD 8.33 BD- Sin 20x8.33 2.55 mi, he BD + DE → momtain height CDG=2000) = 2.65+ 2000 = 2002.55 mi COS B From > DABD AD= AB 8.33 Cos 2o. = 7.63 mi. considhu We have A ACO, to find CD. opposite sich Adiacht sich CD tem <= 793 tan 16= CD 7.53 7.83 CD = tam 16. 5 2.24 mi BC = montanin BD-CD plan Itaight of above BLE 2.85- 2.24 -0.61 mih. tight of montain tright of planne 2002.85 miḥ above montain 0.61 mih